Neural networks
Weights are the adjustable numbers inside a neural network that decide how much each input matters; training is the process of finding good values for them.
Every connection between two neurons has a weight. A big positive weight means 'this input strongly matters, in this direction.' A weight near zero means 'ignore this.' A negative weight flips the effect. All of a model's learned knowledge is stored in these numbers, not as facts or rules a person could read.
Before training, weights are set randomly. During training, each example produces an error, and backpropagation computes how each weight should shift to reduce it. After enough examples, the weights settle into values that make the network useful. Copying a model means copying its weights.
When people talk about a model's size, they mean roughly how many weights it has. A large language model may have hundreds of billions. 'Open weights' means a company has published those numbers so anyone can download and run the model.
On a sound mixing board, each slider sets how loudly one instrument comes through; a network's weights are millions of sliders set automatically by training.